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A202455 Number of (n+2) X 4 binary arrays with consecutive windows of three bits considered as a binary number nondecreasing in every row and column. 1

%I

%S 729,1194,1876,2835,4137,5854,8064,10851,14305,18522,23604,29659,

%T 36801,45150,54832,65979,78729,93226,109620,128067,148729,171774,

%U 197376,225715,256977,291354,329044,370251,415185,464062,517104,574539,636601,703530

%N Number of (n+2) X 4 binary arrays with consecutive windows of three bits considered as a binary number nondecreasing in every row and column.

%C Column 2 of A202461.

%H R. H. Hardin, <a href="/A202455/b202455.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/4)*n^4 + (15/2)*n^3 + (229/4)*n^2 + 237*n + 427.

%F Conjectures from _Colin Barker_, May 31 2018: (Start)

%F G.f.: x*(729 - 2451*x + 3196*x^2 - 1895*x^3 + 427*x^4) / (1 - x)^5.

%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

%F (End)

%e Some solutions for n=4:

%e ..0..0..0..0....0..0..0..0....0..1..0..0....0..0..0..0....0..0..0..0

%e ..0..1..1..1....0..0..0..0....0..1..0..0....0..0..0..0....0..0..1..0

%e ..0..1..1..1....0..0..0..0....0..1..0..0....0..0..0..0....0..0..1..0

%e ..1..1..1..1....0..1..0..1....0..1..1..0....0..0..0..0....0..1..1..0

%e ..1..1..1..1....0..0..1..1....0..1..0..0....0..0..1..0....0..1..1..1

%e ..0..1..1..1....0..0..1..1....1..1..1..1....0..0..0..1....1..1..1..1

%Y Cf. A202461.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 19 2011

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Last modified October 19 09:28 EDT 2018. Contains 316339 sequences. (Running on oeis4.)